A polling firm called Silver Bullet has done a survey of primary voters in the Virginia’s seventh congressional district, who lifted David Brat over House majority leader Eric Cantor last week. Immigration issues — Cantor has been frequently seen as supportive of some form of comprehensive immigration reform and of legal status for some illegal immigrants — seem to have played an important role in the race, but they were not the only factor. (Caveats: The poll has a big sample size, about 800 voters, but it was automated.)

When people who said they voted for Brat were asked which issue “most influenced” their decision to vote for him, they were given four choices. The results:

Twenty-two percent may not sound like much, but it suggests a really outsized role for immigration, which polls usually find is quite far down Americans’ list of political priorities. Of course, it was one of just four options here, so that would boost its importance no matter what. In any case, 22 percent of Brat voters was enough to explain his margin of victory. (This share of people citing immigration as their main issue was also remarkably close to what a pro-comprehensive-immigration-reform group, FWD.us, found in the district.)

Supporters of comprehensive reform will note that a full 48 percent of Brat voters told Silver Bullet that immigration policy was “not significant” to their vote — but 40 percent, a huge number, said it was a “significant part” of their decision to pick the professor, and 12 percent called it the ”main reason.”

Some conservative skeptics of national-security policies suggested that Brat’s criticism of the National Security Agency’s surveillance work helped boost him over Cantor, who tends to be hawkish on foreign-policy issues — the 2 percent of people who named privacy/government surveillance as their top issue seems to suggest this was not relevant.

It seems that there was something of a anti-establishment backlash against Cantor, independent of policy views: A whopping 71 percent primary voters who say they support the Tea Party went for Brat. Sixty-six percent of voters who oppose the Tea Party went for Cantor. (Twenty-six percent of the sample said they had no opinion of the Tea Party.)